A spokesman for the museum located in China's Forbidden City said the missing items include small Western-style makeup cases encrusted with jewels, China's official Xinhua news agency reported.
Feng Nai'en, an assistant curator, said a suspicious man being questioned by a museum staff member fled Sunday night after authorities were called.
Staff and armed police searched for the man but he apparently escaped with some pieces.
Two of the missing relics have been recovered but both were slightly damaged, Feng said.
He said the Palace Museum has issued a formal apology to the Hong Kong museum and is increasing security for the exhibit.
There was no information on the value, number or age of the missing items.
The last theft at the Palace Museum was in 1991.